Radio frequency (RF) spectrum is a scarce resource. In the cellular or personal communications systems (PCS) environment an increasing number of users needs to be serviced at the same time avoiding simultaneous users interfering with each other. One way to pack multiple simultaneous users on the same frequency band is spatial division multiple access (SDMA). The purpose of SDMA is to separate the radio signals of interfering users (either intentional or accidental) from each others on the basis of the differing spatial characteristics of different user signals. One example of these characteristics is the arrival direction of the signal. The separation may be accomplished using an array of antennas at the basestation and filters attached to each antenna signal. The filters are learned on the basis of the user signals, rejecting unwanted signals while enhancing the desired signal.
These methods can be divided into two groups on the basis of whether they use training signals or not. Training signal methods typically use a variant of a least mean squares (LMS) algorithm to adapt the coefficients of the filters. This is usually a robust way of estimating the channel. One disadvantage of training signal methods, however, is that a large part of the signal needs to be wasted as predetermined training data. Further, the methods might not be fast enough for rapidly varying fading channels.
Unsupervised methods, methods not using training signals, rely on either information about the antenna array manifold or properties of the signals themselves. Mainstream unsupervised approaches are of the former type. Methods relying on antenna array manifold information often require calibrated antenna arrays, special array geometries, or they might also set serious limitations on the propagation environment. Less restrictive methods make use of the signal properties only. Some possible signal properties include constant modulus, finite alphabet, spectral self-coherence, cyclostationarity, or other statistical properties. Blind source separation (BSS) techniques typically are the least restrictive. BSS techniques rely only on source signal independence and non-Gaussianity assumptions. BSS denotes observing mixtures of independent sources, and by making use of these mixed signals only and nothing else, recovering the original or source signals.
The separation of independent sources from an array of sensors is a classic but difficult problem in signal processing. Generally, the signal sources as well as their mixture characteristics are unknown. Without knowledge of the signal sources, other than a general assumption that the sources are independent, the signal processing is commonly known in the art as the "blind separation of sources". The separation is "blind" because nothing is assumed about the independent source signals, nor about the mixing process.
A typical example of the blind separation of source signals is where the source signals are sounds generated by two independent sources, such as two (or more) separate speakers. An equal number of microphones (two in this example) are used to produce mixed signals, each composed as a weighted sum of the source signals. Each of the source signals is delayed and attenuated in some unknown amount during passage from the speaker to a microphone, where it is mixed with the delayed and attenuated components of the other source signals. Multi-path signals, generated by multiple reflections of the source signals, are further mixed with direct source signals. This is generally known as the "cocktail party" problem, since a person generally wishes to listen to a single sound source while filtering out other interfering sources, including multi-path signals.
Those skilled in the signal processing arts have been eager to solve blind source separation problems because of their broad application to many communication fields. In the cellular telecommunications art, for example, a receiver must eliminate interfering signals from neighboring cells (or the same cell in the case of SDMA) to avoid unacceptable levels of interference.
Generally, the art is concerned with a static linear signal mixing model. The art has been applied to separation of multiple audio, biomedical, and accelerometer signals; however, not to sources such as radio signals in a mobile environment that carry digital information. The art also assumes that the statistical properties of the signals remain stationary and that the mixing process remains stationary. The first assumption holds true in radio communications in general, but the latter assumption does not apply to mobile communications, which today forms a large portion of overall radio communications. The latter assumption does not apply to mobile communications because as the term suggests, in mobile communications the users are constantly moving causing nonstationary mixing conditions. There is thus a need for BSS methods that do not assume that the mixing process remains stationary.
In mobile communications the signals are subject to fading. Usually there is no direct line of sight from the transmitter to the receiver, only multiple reflected and diffracted signal components reach the receiver. For example, referring briefly to FIG. 2 obstacles, such as buildings 40, interfere with a signals path and create reflections. When either the receiver or the transmitter is moving, for example, in an urban environment, building reflections are changing very rapidly.
Thus methods for SDMA that are based on finding the directions of the mobile transmitters do not work in general, because these are the directions of just multiple reflections, and they vary rapidly. Thus there is a need for methods of separating radio signals that are not based on the concept of direction, but that work in a blind fashion.
If the phases of the carrier signals in the multipath components are aligned, the components add constructively at the receiver. If the phases of carriers are 180 degrees off, the components add destructively. Note that a difference of a half a wavelength of the carrier frequency in the distance between the transmitter and the receiver corresponds to a 180 degree phase shift. This is only about a half foot at 900 megahertz (Mhz). Because this small a difference in relative positions can cause the signal going from constructive interference to a null received signal, the result is that both the amplitude and the phase of the received signal vary seemingly randomly at a rate that is proportional to relative speeds of the transmitter and the receiver. The amplitude of the received signal follows a Rayleigh distribution, hence the name Rayleigh fading. For example, assuming 60 mph relative speed of the transmitter and the receiver, it only takes 5 milliseconds for the received signal to change from a peak of the amplitude into a deep fade, where the amplitude can be as much as 20 to 30 dB lower than at the peak. Assuming a transmitted symbol rate of 20000 symbols/second, this corresponds to a mere 100 received symbols during this change.
Accordingly, there exists a need for a blind separation method that can adapt to these rapidly changing conditions keeping up with the fading rate. Without the ability to adapt to rapidly changing conditions, BSS techniques will not be a feasible basis for SDMA in cellular communications.